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KahanMath (Complex Research 1.0 API)
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oe.math.complex.research.util</FONT>
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Class KahanMath</H2>
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<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>oe.math.complex.research.util.KahanMath</B>
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<DL>
<DT><PRE>public final class <B>KahanMath</B><DT>extends <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
Utility functions from the "Branch cuts for complex elementary functions" by Prof. Kahan.
<P>

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<B>Field Summary</B></FONT></TH>
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<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#OVERFLOW_THRESHOLD">OVERFLOW_THRESHOLD</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Ω := Overflow threshold = Nextafter(+∞, 0).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#ROUNDOFF_THRESHOLD">ROUNDOFF_THRESHOLD</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ε := Roundoff threshold = 1.0 - Nextafter(1.0, 0).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#UNDERFLOW_THRESHOLD">UNDERFLOW_THRESHOLD</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;λ := Underflow threshold = 4(1-ε)/Ω.</TD>
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<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#abs(double, double, oe.math.complex.research.util.KahanConstants)">abs</A></B>(double&nbsp;x,
    double&nbsp;y,
    <A HREF="../../../../../oe/math/complex/research/util/KahanConstants.html" title="enum in oe.math.complex.research.util">KahanConstants</A>&nbsp;constants)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#addWithPresubstitute(double, double)">addWithPresubstitute</A></B>(double&nbsp;a,
                     double&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#arg(double, double)">arg</A></B>(double&nbsp;x,
    double&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#cdiv(double, double, double, double)">cdiv</A></B>(double&nbsp;u,
     double&nbsp;v,
     double&nbsp;x,
     double&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#clogs(double, double, int)">clogs</A></B>(double&nbsp;x,
      double&nbsp;y,
      int&nbsp;j)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#cmult(double, double, double, double)">cmult</A></B>(double&nbsp;u,
      double&nbsp;v,
      double&nbsp;x,
      double&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#corner(double, double)">corner</A></B>(double&nbsp;x,
       double&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#csqrt(double, double)">csqrt</A></B>(double&nbsp;x,
      double&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#cssqs(double, double)">cssqs</A></B>(double&nbsp;x,
      double&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#logb(double)">logb</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#multiplyWithPresubstitute(double, double)">multiplyWithPresubstitute</A></B>(double&nbsp;a,
                          double&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../oe/math/complex/research/util/KahanMath.html#subtractWithPresubstitute(double, double)">subtractWithPresubstitute</A></B>(double&nbsp;a,
                          double&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
</TABLE>
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<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
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<A NAME="OVERFLOW_THRESHOLD"><!-- --></A><H3>
OVERFLOW_THRESHOLD</H3>
<PRE>
public static final double <B>OVERFLOW_THRESHOLD</B></PRE>
<DL>
<DD>Ω := Overflow threshold = Nextafter(+∞, 0).
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#oe.math.complex.research.util.KahanMath.OVERFLOW_THRESHOLD">Constant Field Values</A></DL>
</DL>
<HR>

<A NAME="ROUNDOFF_THRESHOLD"><!-- --></A><H3>
ROUNDOFF_THRESHOLD</H3>
<PRE>
public static final double <B>ROUNDOFF_THRESHOLD</B></PRE>
<DL>
<DD>ε := Roundoff threshold = 1.0 - Nextafter(1.0, 0).
<P>
<DL>
</DL>
</DL>
<HR>

<A NAME="UNDERFLOW_THRESHOLD"><!-- --></A><H3>
UNDERFLOW_THRESHOLD</H3>
<PRE>
public static final double <B>UNDERFLOW_THRESHOLD</B></PRE>
<DL>
<DD>λ := Underflow threshold = 4(1-ε)/Ω.
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#oe.math.complex.research.util.KahanMath.UNDERFLOW_THRESHOLD">Constant Field Values</A></DL>
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<A NAME="corner(double, double)"><!-- --></A><H3>
corner</H3>
<PRE>
public static double[] <B>corner</B>(double&nbsp;x,
                              double&nbsp;y)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="multiplyWithPresubstitute(double, double)"><!-- --></A><H3>
multiplyWithPresubstitute</H3>
<PRE>
public static double <B>multiplyWithPresubstitute</B>(double&nbsp;a,
                                               double&nbsp;b)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="addWithPresubstitute(double, double)"><!-- --></A><H3>
addWithPresubstitute</H3>
<PRE>
public static double <B>addWithPresubstitute</B>(double&nbsp;a,
                                          double&nbsp;b)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="subtractWithPresubstitute(double, double)"><!-- --></A><H3>
subtractWithPresubstitute</H3>
<PRE>
public static double <B>subtractWithPresubstitute</B>(double&nbsp;a,
                                               double&nbsp;b)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="logb(double)"><!-- --></A><H3>
logb</H3>
<PRE>
public static double <B>logb</B>(double&nbsp;x)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="cmult(double, double, double, double)"><!-- --></A><H3>
cmult</H3>
<PRE>
public static double[] <B>cmult</B>(double&nbsp;u,
                             double&nbsp;v,
                             double&nbsp;x,
                             double&nbsp;y)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="cdiv(double, double, double, double)"><!-- --></A><H3>
cdiv</H3>
<PRE>
public static double[] <B>cdiv</B>(double&nbsp;u,
                            double&nbsp;v,
                            double&nbsp;x,
                            double&nbsp;y)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="abs(double, double, oe.math.complex.research.util.KahanConstants)"><!-- --></A><H3>
abs</H3>
<PRE>
public static double[] <B>abs</B>(double&nbsp;x,
                           double&nbsp;y,
                           <A HREF="../../../../../oe/math/complex/research/util/KahanConstants.html" title="enum in oe.math.complex.research.util">KahanConstants</A>&nbsp;constants)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="arg(double, double)"><!-- --></A><H3>
arg</H3>
<PRE>
public static double[] <B>arg</B>(double&nbsp;x,
                           double&nbsp;y)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="cssqs(double, double)"><!-- --></A><H3>
cssqs</H3>
<PRE>
public static double[] <B>cssqs</B>(double&nbsp;x,
                             double&nbsp;y)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="csqrt(double, double)"><!-- --></A><H3>
csqrt</H3>
<PRE>
public static double[] <B>csqrt</B>(double&nbsp;x,
                             double&nbsp;y)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="clogs(double, double, int)"><!-- --></A><H3>
clogs</H3>
<PRE>
public static double[] <B>clogs</B>(double&nbsp;x,
                             double&nbsp;y,
                             int&nbsp;j)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
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